Follows by the proof of uncloneable security of conjugate encryption given in [1]}See Lemma 14 and Corollary 2 in [1]} with proofs.. It turns out that the success probability of a cloning adversary equals that of a ROMG adversary, which is restricted in preparing the state \(\rho _{ABC}\)  to create an EPR pair and apply the splitting map \(\Phi \)  to the \(BC\)  register. We only need Lemma REF  for this proof to go through, as the EPR pair then does not depend on the state, before and after the splitting.
